The circular polarizers were mostly made of meta-atom based chiral metamaterials (CMMs). Here we propose an ultra-thin metallic grating based circular polarizer, which can convert any polarization into circular polarization. The circular polarizer consists of two layers: an ultra-thin metallic grating embedded in the substrate and a silicon grating on the substrate surface. The ultra-thin metallic grating, which is thinner than the skin depth and was shown to hold anomalous resonant reflection for transverse magnetic (TM) wave, functions as a quarter-wave plate. We show that the ultra-thin metallic grating based quarter-wave plate can transmit circular polarized wave when the incident linear polarized wave is oriented properly. The silicon grating acts as a linear polarizer which restricts the polarization of the light that reaches the metallic grating. Unlike some of the CMMs, our structure is independent of the incident polarization state. Moreover, the fabrication of our circular polarizer is easier than other double-layer-CMMs, in which the relative position between the two layers must be precisely controlled. Our structure can find its application integrated photonic devices.
In the final optics assembly of Inertial Confinement Fusion (ICF) driver, Diffractive Optical Elements (DOEs) are applied to achieve some important functions, such as harmonic wave separation, beam sampling, beam smoothing and pulse compression etc. However, in order to optimize the system structure, decrease the energy loss and avoid the damage of laser induction or self-focusing effect, the number of elements used in the ICF system, especially in the final optics assembly, should be minimized. The multiple exposure method has been proposed, for this purpose, to fabricate BSG and CSG on one surface of a silica plate. But the multiple etch processes utilized in this method is complex and will introduce large alignment error. Error diffusion method that based on pulse-density modulation has been widely used in signal processing and computer generated hologram (CGH). In this paper, according to error diffusion method in CGH and partial coherent imaging theory, we present a new method to design coding mask of combine CSG-BSG element with error diffusion method. With the designed mask, only one exposure process is needed in fabricating combined element, which will greatly reduce the fabrication difficulty and avoid the alignment error introduced by multiple etch processes. We illustrate the designed coding mask for CSG-BSG element with this method and compare the intensity distribution of the spatial image in partial coherent imaging system with desired relief.
In this paper, a new focusing method adopting an axicon for the demand of the plasma measurements in inertial confinement fusion (ICF) drivers is presented. In order to improve the performance of this element, annular-aperture and Super-Guassian apodization are introduced to remove the on-axis oscillations. Meanwhile, the lateral width is optimized through choosing appropriate radius ratio of the inner ring to outer ring of the element. Furthermore, the feasibility is conformed by numerical evaluation of Fresnel diffraction integral .The results obtained are accordant with our designed intention. At last, as an example and for specific application, we designed an axicon, which has almost unchanged axial intensity, a focal depth more than 3mm, beam size smaller than 100μm and the maximal relative intensity of side lobe less than 2%. The performance of this element satisfies the requirements of plasma measurements in ICF drivers.
In high power laser system, it is of great interest to combine two or more diffractive structures, in particular, the beam-sampling gratings (BSG) and the color separation gratings (CSG), onto one element. However, the combined element with diffractive structure on both surfaces, may cause serious laser induced damage to the element itself. So, this paper use Fourier modal method to analyze the near field characteristic of CSG and BSG combined element. Through theoretically analysis and numerical calculation, amplitude and phase distribution of electric field are present both inside and outside the diffractive structural region, and the maximum peak-to-average modulation in near field is also given. Based on this study, the most possibility of optical damage induced by beam modulation of CSG and BSG combined element appears in the neighborhood of the interface.
Diffractive gratings, such as 1 grating and beam sampling grating (BSG), are used in the inertial confinement fusion (ICF) driver because of their high diffractive efficiency. Under high power laser condition, it demands that near fields of the diffractive gratings, mainly affected by input laser energy and beam modulation, must be less than their damage threshold, otherwise the diffractive gratings will be damaged. In this paper, Fourier modal method based on the rigorous electromagnetic theory is introduced to rapidly and accurately analyze the distribution of near fields of the diffractive gratings. Its physical concept is clear and concise, and computation cost is small. Through numerical simulation, it indicates that the results calculated by Fourier modal method are accurate and effective, compared with those calculated by other method. The near fields of 1 grating used in final optical system of ICF driver are obtained. In addition, fabrication errors effects on the near field modulation are simulated. It shows that the sidewall slope errors are the main cause of optical field modulation. With theoretical analysis and numerical simulation, it is useful to understand mechanism of damage and help how to control fabrication process errors of the optical elements used in the optical system of ICF.
Proc. SPIE. 5636, Holography, Diffractive Optics, and Applications II
KEYWORDS: Diffractive optical elements, Modulation, High power lasers, Error analysis, Near field, Near field diffraction, Optical damage, Laser systems engineering, Diffraction gratings, Amplitude modulation
Color Separating Grating (CSG) is one of the important Diffractive Optical Elements (DOE) used in the final optical system of high power laser system. Its periodic step-phase structure can separate the third harmonic frequency from base- and second-harmonic waves in the far field. But the structure abbreviations of CSG, caused by the fabrication process, generate great modulations to the laser beam, which may lead to severe optical damages to CSG itself and the system. In this paper, a comprehensive error model is built, in which each structural parameter of CSG is expressed as a variable, and the structural parameter error induced by fabrication process is expressed as minute disturb of relative variable. With this error model, the near field diffraction pattern of CSG is calculated based on Fresnel diffractive theory. Through simulation and analysis, we obtain the amplitude modulation of different harmonic waves in near field, and also the relationship between the amplitude modulation and the fabrication error. The results show that beam modulations are mainly caused by the stair depth error and the slope error. This study provides a convenient way to estimate the possibility of optical damages induced by CSG.
In the final optics assembly of ICF driver, Diffractive Optical Elements (DOEs) are applied to achieve some important functions. Due to the advantage of easy integration, DOEs that achieve different functions can be combined into one element, and thus the system structure and performance of ICF driver can be optimized. In this paper, we present a new means to fabricate color separation grating (CSG) and beam sampling grating (BSG) on two surfaces of one fused-silica substrate with two-surface exposure method. The mask for CSG can be fabricated with common optical method since the period of CSG is large; whereas the mask for BSG cannot be made with normal micro-fabrication system whose resolution cannot meet the requirement of fabrication precision of slowly changed BSG fringes (from 2μm to 4μm). Therefore, we use e-beam direct writing method to fabricate mask for BSG. The alignment of CSG and BSG is designed in accordance with the requirement of actual system. Thus the functions of harmonic wave separation and beam sampling are realized through one silica plate. The satisfying experimental results are illustrated.
Grating lenses are diffractive optical elements with gradually variant space and line, and are widely applied to various optical systems, such as harmonic wave separation and diagnosis of high power laser system, optical communication and spectral analysis. Because of its small feature size (just about several times of the illumination wavelength) and gradually variant space and line, the simulation results are not accurate when using the scalar diffractive theory. In this paper, the grating lenses are subdivided into smaller areas, and every sub-area is regarded as periodic microstructure because variance of adjacent period is very small. Then Fourier modal method is adopted to analyze their diffractive properties in sequence, and finally total diffractive efficiency of grating lenses can be easily obtained. Its physical concept is clear and concise, and computation cost is small. Through numerical simulation, diffractive efficiency of grating lens for beam sampling and harmonic separation in high power laser system is calculated. It indicates that the method presented in this paper is accurate and valid. In addition, fabrication errors effects on diffractive efficiency are also simulated in order to obtain the relationship between process errors and diffractive efficiency of grating lenses. It suggests that grating lenses not only can be easily realized in fabrication process, but also can meet practical demand in high power laser system. In experiment, a beam-sampling grating with diameter 100 mm was fabricated, and its experimental diffractive efficiency is consistent with result calculated by the method in this paper.
A maskless lithography imaging simulation using digital micromirror device (DMD) was investigated. The DMD acts as a reflective spatial light modulator. The micro-mirrors on DMD can be instructed by the computer to tilt them ±12° off their normal position which produces a mask pattern, and then the mask pattern can be carried onto the surface of wafer by the imaging system. Because the imaging of the maskless lithography is a complex process, it is necessary to simulate and analyze its practical process. In this paper, we present a partial coherent imaging model of maskless lithography considering the practical projection characterization of DMD. With the model, it is convenient to simulate the lithography of arbitrarily shaped microstructure using DMD. Through calculation, the spatial image in maskless lithography process based on gray scale photolithography with DMD real-time masks was obtained.
The CSG’s physical performance is decided by its structural parameters, such as width of grating stair, height of grating
stair, and the shape of stair edge. Consideration of the practical fabrication process, an error model of CSG’s structure is built to express the relationship between CSG’s performance and its structural parameters. In this model, each structural parameter of CSG is expressed as a variable, and the structural parameter error induced by fabrication process is expressed as minute disturb of relative variable. Through analysis and simulation, we obtained a general estimation standard for the structural parameter errors of CSG, which provides a theoretical direction for CSG’s fabrication and usage.
An optimized coding gray-tone mask method with multi-parameters is presented in this paper. Precise calculations, which are performed on the dead area in the backward reflection of the pyramid prism, demonstrate that the fringe error caused by the coding gray-tone mask has little affect on the performance of the pyramid prisms. This not only greatly reduce the resolution requirement of the coding gray-tone mask, but also reduce the errors produced by the exposure
process. A satisfying simulation result is obtained with the designed coding gray-tone mask.
Proc. SPIE. 4924, Holography, Diffractive Optics, and Applications
KEYWORDS: Electronics, High power lasers, Phase shift keying, Laser beam propagation, Adaptive optics, Near field, Optical simulations, Optics manufacturing, National Ignition Facility, Laser systems engineering
Based on the analysis of phase aberrations in high power laser system, the phase corrector plate is presented to correct the static phase aberration. It can greatly improve the performance of the focal spot and is regarded as the suitable supplement of adaptive optics. In this paper, the performance of phase corrector plate, both continuous structure and multi-steps structure, is analyzed and simulated. The effect of misalignment between the phase corrector plate and the laser beam on the focal spot is also presented and simulated.
Digital implementation of fractional Fourier transform hologram (FRTH) is studied. From the definition of fractional Fourier transform (FRT), its discrete form is obtained and then a fast FRT algorithm is generated based on fast Fourier transform (FFT). Therefore, with the algorithm whose numerical efficiency is equal to the FFT, FRT can be quickly calculated and moreover FRTCGH can be efficiently encoded and reconstructed. The digital implementation for FRTH can lead its advantages, such as flexibility of fabrication and variation with recording system parameters, to expanding its application fields in FRT and holography.
A new method is presented to encode and decode images with computer-generated hologram of fractional Fourier transform. The fractional Fourier transform computer-generated holograms (FRT-CGH) of several objects with different orders are respectively recorded on one holographic plate. In order to reconstruct images of the objects, several fractional Fourier transform systems of certain orders are needed. This method is agile and convenient on design and fabrication. It can be encoded and decoded either by numerical method or by optical method. Because of its particularity of image reconstruction, FRT-CGH is regarded as a new optical security system and may be widely used in the future.
The beam sampling grating is one of the important diffractive optical elements used in the field of laser sampling. It can be considered as an off-axis, binary phase, Fresnel zone plate. Base don the theory of interference, the principle of the variable period grating formation process is analyzed perfectly and the transmissive function of the BSG is obtained. This paper repots to fabricate the BSG with electron-beam direct writing. Compared with the holographic method, the new method is simpler, cheaper, and more efficient to manufacture elements on a large scale.
FRTH is a new kind of hologram, which is different form common Fresnel holograms and Fourier transform holograms. It can be applied for fractional Fourier transform filtering and anti-counterfeiting, etc. Due to the flexibility of holographic lens, we present a method that uses the -1 diffraction wave of holographic lens as the object wave and the 0 diffraction wave as the reference wave to record FRTH. It provides a new simple way to record FRTH. In this paper, the theory of achieving FRT and recording FRTH with holographic lens has been discussed, and the experimental results are also presented.
In this paper, we introduce the recording and reconstruction theories of the multiple fractional Fourier transform hologram (M-FRTH). We fabricated a multiple fractional Fourier transform hologram, and obtained satisfying reconstruction results. The experimental result shows that the M-FRTH has a high anti-counterfeiting capacity and can be used in the fabrication of the trademark, ID, and the notes.
A new method has been developed to fabricate refractive microlens by etching ammonium dichromate gelatin (ADG) with enzyme solution. Unlike previous methods which are used to fabricate refractive microlens with photoresist, the process of fabricating microlens by etching ADG with enzyme solution doesn't require the use of expensive equipment, and it isn't sophisticated and time consuming. The light exposes ADG through a high contrast binary mask, then the exposed parts of ADS generate cross- linking reaction. Usually, the relief achieved by water developing is very shallow (<1um) when nonpre-harden gelatin is used, so we compound a certain concentration enzyme solution, and because of surface tension, ADG turns to spherical structure after developing. The optimum technique parameters of this process are presented. Results are presented for experiments and evaluated by profile meter and interference microscope.
Based on the energy conservation law, a modified proximity function is proposed to describe the absorbed energy distribution in photoresist during laser writing. The measured data for photoresist absorbing energy are fitted well to the modified proximity function. We analyze the proximity effect in laser writing by using the new model, it is helpful to further develop the precompensation and multi- exposure methods to correct proximity effects in laser direct writing.
The fabrication of refractive microlens by introducing the melting process with coding gray-tone mask is reported. The applied mask is obtained by the coding method, nonlinear effects in intensity distribution through the gray-tone mask have been taken into account to correct the mask design. A continuous relief is formed in photoresist after exposing, and then the excellent surface shape microlens can be gained by melting. The technical parameters of this process are also presented. Results are presented for experiments and evaluated by profile meter and scanning electronic microscope. The fabrication technology of refractive microlens by this process is simple and it indicates the enormous potential to extend the fabrication range ofrefractive microlens.
A new method is proposed to design gray-tone masks for fabrication of surface relief microstructures. Unlike previous methods which modulate the light intensity by changing the cell size or cell pitch only, the method relays on adjusting both the shape and position of a cell which gives an extra freedom to control the design accuracy. Using the new method a gray-tone mask has been designed to produce a hemispherical shape relief structure. Based on the theory of partial coherent light and the resist development model, the intensity distribution through the gray-tone mask and exposure of photoresist have been simulated. Nonlinear effects in aerial image and resist development have been taken into account to correct the mask design. The accuracy of the gray-tone mask design has been confirmed by simulation of 3D resist profiles.
In fogging, using laser and CCD sensor (charge coupled device) measuring, because of scattering effect to laser and other light, the output signal from CCD is not stable and make errors. For example, measuring the diameter of cable by laser and CCD on vulcanization line, there is vapor around cable, so it can produce water bead and line on cable and window used to observe. The fogging and water make the measure result neither stable nor accuracy. A special signal processing method of CCD which combines soft-ware with hard-ware is deeply discussed in this paper. The experiment has proved that this method to measure the diameter of cable is absolutely feasible and very successful.